Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916957785161728 |
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| author | Sarhil, Mohammad Shchyglo, Oleg Salama, Hesham Brands, Dominik Steinbach, Ingo Schröder, Jörg |
| author_facet | Sarhil, Mohammad Shchyglo, Oleg Salama, Hesham Brands, Dominik Steinbach, Ingo Schröder, Jörg |
| contents | To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in obtaining the mechanical driving forces of phase-field evolution. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields associated to their pairwise normals, except in the dual-phase-field regions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces as a function of pairwise strains. These ad hoc pairwise definitions enable us to satisfy the static equilibrium and kinematic compatibility conditions between all the locally-active phase-fields. Different numerical examples are presented, which compare the developed model against the equal-strain and equal-stress limiting cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02406 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces Sarhil, Mohammad Shchyglo, Oleg Salama, Hesham Brands, Dominik Steinbach, Ingo Schröder, Jörg Numerical Analysis To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in obtaining the mechanical driving forces of phase-field evolution. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields associated to their pairwise normals, except in the dual-phase-field regions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces as a function of pairwise strains. These ad hoc pairwise definitions enable us to satisfy the static equilibrium and kinematic compatibility conditions between all the locally-active phase-fields. Different numerical examples are presented, which compare the developed model against the equal-strain and equal-stress limiting cases. |
| title | Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2304.02406 |